{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3VVMELQTMDDQNSDGW5AWEAYNKW","short_pith_number":"pith:3VVMELQT","schema_version":"1.0","canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","source":{"kind":"arxiv","id":"1403.3525","version":1},"attestation_state":"computed","paper":{"title":"Additive solvability and linear independence of the solutions of a system of functional equations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AC","authors_text":"Eszter Gselmann, Zsolt P\\'ales","submitted_at":"2014-03-14T10:47:39Z","abstract_excerpt":"The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \\[d_{k}(xy)=\\sum_{i=0}^{k}\\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \\qquad (x,y\\in \\R,\\,k\\in\\{0,\\ldots,n\\}) \\] is studied, where $\\Delta_n:=\\big\\{(i,j)\\in\\Z\\times\\Z\\mid 0\\leq i,j\\mbox{and}i+j\\leq n\\big\\}$ and $\\Gamma\\colon\\Delta_n\\to\\R$ is a symmetric function such that $\\Gamma(i,j)=1$ whenever $i\\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\\dots,d_{n}\\colon \\R\\to\\R$ of the above system of equations is characterized. As a consequen"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.3525","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"360ec3231c6c41949d8963fe933ad685ec1c7fe06229ac8f1e0c622fc3c029e2","abstract_canon_sha256":"c91e657a81f28d346970fe6988122f3d6054dca6c38babf751c4cbea4edca9de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:20.236277Z","signature_b64":"G7k7gYM2QDqmZMe82aWJ4OaCDQYjodJdrTYq2SMyHajpi4xWs420xOWvr6zILDc/44784m01zO/HBgdlKT4QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","last_reissued_at":"2026-05-18T02:56:20.235552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:20.235552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Additive solvability and linear independence of the solutions of a system of functional equations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AC","authors_text":"Eszter Gselmann, Zsolt P\\'ales","submitted_at":"2014-03-14T10:47:39Z","abstract_excerpt":"The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \\[d_{k}(xy)=\\sum_{i=0}^{k}\\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \\qquad (x,y\\in \\R,\\,k\\in\\{0,\\ldots,n\\}) \\] is studied, where $\\Delta_n:=\\big\\{(i,j)\\in\\Z\\times\\Z\\mid 0\\leq i,j\\mbox{and}i+j\\leq n\\big\\}$ and $\\Gamma\\colon\\Delta_n\\to\\R$ is a symmetric function such that $\\Gamma(i,j)=1$ whenever $i\\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\\dots,d_{n}\\colon \\R\\to\\R$ of the above system of equations is characterized. As a consequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3525","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.3525","created_at":"2026-05-18T02:56:20.235665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3525v1","created_at":"2026-05-18T02:56:20.235665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3525","created_at":"2026-05-18T02:56:20.235665+00:00"},{"alias_kind":"pith_short_12","alias_value":"3VVMELQTMDDQ","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3VVMELQTMDDQNSDG","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3VVMELQT","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW","json":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW.json","graph_json":"https://pith.science/api/pith-number/3VVMELQTMDDQNSDGW5AWEAYNKW/graph.json","events_json":"https://pith.science/api/pith-number/3VVMELQTMDDQNSDGW5AWEAYNKW/events.json","paper":"https://pith.science/paper/3VVMELQT"},"agent_actions":{"view_html":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW","download_json":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW.json","view_paper":"https://pith.science/paper/3VVMELQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3525&json=true","fetch_graph":"https://pith.science/api/pith-number/3VVMELQTMDDQNSDGW5AWEAYNKW/graph.json","fetch_events":"https://pith.science/api/pith-number/3VVMELQTMDDQNSDGW5AWEAYNKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/action/storage_attestation","attest_author":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/action/author_attestation","sign_citation":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/action/citation_signature","submit_replication":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/action/replication_record"}},"created_at":"2026-05-18T02:56:20.235665+00:00","updated_at":"2026-05-18T02:56:20.235665+00:00"}